Question

Two students were testing the parachute designs they made for an egg-drop project. Both students dropped their eggs from a height of 10 feet. One design made the egg fall at a rate 5 feet per second, and the other design made the egg fall at a rate of 3 feet per second. If x represents the time in seconds that the egg falls and y represents the height of the egg, which system of equations represents the situation described?(1 point)
Responses

{y=−5xy=−3x
enlarged left brace start layout first row y equals negative 5 x second row y equals negative 3 x end layout

{y=10−5xy=10−3x
enlarged left brace start layout first row y equals 10 minus 5 x second row y equals 10 minus 3 x end layout

{y=5x−10y=3x −10
enlarged left brace start layout first row y equals 5 x minus 10 second row y equals 3 x minus 10 end layout

{y=10+5xy=10+3x

Answer 1

To represent the situation of the egg-drop project using a system of equations, we need to establish the relationship between height \( y \), time \( x \), and the rate of descent for each student's design.

For the eggs dropped from a height of 10 feet, the height \( y \) decreases over time.

1. For the first design, which makes the egg fall at a rate of 5 feet per second, the height can be expressed as:
\[
y = 10 - 5x
\]
Here, \( 10 \) is the initial height, and \( 5x \) is the distance fallen after \( x \) seconds.

2. For the second design, which makes the egg fall at a rate of 3 feet per second, the height can be expressed as:
\[
y = 10 - 3x
\]
Similarly, \( 10 \) is the initial height, and \( 3x \) is the distance fallen after \( x \) seconds.

Putting these two equations together, we have the following system of equations:
\[
\begin{cases}
y = 10 - 5x \\
y = 10 - 3x
\end{cases}
\]

Thus, the correct response that represents the described situation is:
\[
\{ y = 10 - 5x, \ y = 10 - 3x \}
\]